Solve the following integral. The answer can be determined by rules of antidifferentiation, but some algebra may be required beforehand. \( \int \frac{x^{3}-125}{x-5} d x \)

Residues at Poles = Proof the Theorem Assume \( f(z) \) has the following form \[ f(z)=\frac{\phi(z)}{\left(z-z_{0}\right)^{m}} \] where \( \varphi(\mathrm{z}) \) is analytic and nonzero at \( \mathrm{z}_{0} \), then it has Taylor series representation

June 2018 ZIMSEC Paper 1 Solve the equations: \( e^{2 x}=4 e^{2-x} \) giving the answer in exact form. November 2010 ZIMSEC Paper 1

Find the derivative of \( f(w)=\frac{3}{\left(w^{2}-6\right)^{5}} \)

Calcule a integral definida \( \int_{0}^{3} (2x^2 + 4) \, dx \).

3.2. \( \int \ln 3 x d x \)